if n is a prime number than n +1 is not . True or false

True.

Explanation:
To determine if the statement is true or false, we can use the definition of prime numbers.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, it cannot be divided evenly by any other number other than 1 and itself.

Now, let's consider the case when n is a prime number. Since n is a prime number, it has no divisors other than 1 and itself.

If n + 1 were a prime number, it would also have no divisors other than 1 and itself. However, we can see that n + 1 is divisible by 2 (since n is odd, n + 1 will be even and divisible by 2).

Therefore, if n is a prime number, n + 1 cannot be a prime number. Hence, the statement "if n is a prime number than n + 1 is not" is true.

The only even prime is the number 2

so for all prime numbers n>2, n has to be odd
Therefore n+1 is even, and all even numbers except 2 are NOT prime.
So .....